In some aspects of military work, access to blurred messages occurs. The need to read these occasional anomalies is obvious but present means often require time-consuming digital procedures using the various algorithms such as LaPlacian, high-pass filtering and others currently available.
One of the "standard" approaches of both optical and digital is to use an inverse filter. That is, in an optical system or its digital equivalent, one takes a Fourier Transform of the blurred image and places a filter whose character is to be determined in the Fourier or spatial frequency plane. If properly designed, the filter upon reimaging (taking another Fourier Transform) will bring a degree of restoration to the image, rendering it understandable. That means perfect restoration (in one or more operations) is not necessary, or sometimes not even possible. The basis of restoration is summarized in the following sequence of equations: ##EQU1## where the capital letters refer to the Fourier Transforms of the corresponding functions and (*) denotes convolution. The result, in principle, is the inverse filter which, when inserted in the Fourier plane, should provide image restoration.
In FIGS. 1A and 1B we can see pictorially what is done. In FIG. 1A we have the absolute value of amplitude for an image with the modulus of the inverse filter shown in FIG. 1B. In the simplest case the first and third orders would have negative phase and the second and fourth, positive. In reality the spectrum amplitude and phase are much more complicated in distribution throughout the spatial frequency domain.
Much work has been and is being done principally in the digital analysis world with such techniques as contrast enhancement routines, constrained least squares filtering, extended filters, optimizing mean square error filters, and other extensions or alterations of the Wiener filter. The work also includes the standard digital fare like high-pass filtering with convolution matrices, establishing median filters wherein each pixel is processed by giving it the median of its eight neighbors (in a 3.times.3 matrix) and Kalman filtering with various kernels. In others, adaptive filtering is performed. This is a technique of performing a large number of iterations of, in sequence, the Fourier Transform, assessment, modification, inverse transform, assessment, Fourier Transform, modification, and so forth. A priori knowledge or good guessing drive the modifications in the sequence. In some iterative routines, the investigator assumes that the degration must lie between or within a set of parameters and uses these to make appropriate modifications based upon this.